Functional and Condensed Problem Inputs
Note that the initial condition can be written as a function of parameters and initial time:
and be resolved before going to the solver. Additionally, the initial condition can be a distribution from Distributions.jl, in which case a sample initial condition will be taken each time
solve is called.
tspan supports the following forms. The single value form
t is equivalent to
(zero(t),t). The functional form is allowed:
which outputs a tuple.
prob = ODEProblem((u,p,t)->u,(p,t0)->p,(p)->(0.0,p),(2.0,1.0)) using Distributions prob = ODEProblem((u,p,t)->u,(p,t)->Normal(p,1),(0.0,1.0),1.0)
At the high level, known problematic problems will emit warnings before entering the solver to better clarify the error to the user. The following cases are checked if the solver is adaptive:
- Integer times warn
- Dual numbers must be in the initial conditions and timespans
- Measurements.jl values must be in the initial conditions and timespans
If there is an exception to these rules, please file an issue. If one wants to go around the high level solve interface and its warnings, one can call
Modification of problem types
Problem-related types in DifferentialEquations.jl are immutable. This helps, e.g., parallel solvers to efficiently handle problem types.
However, you may want to modify the problem after it is created. For example, to simulate it for longer timespan. It can be done by the
prob1 = ODEProblem((u,p,t) -> u/2, 1.0, (0.0,1.0)) prob2 = remake(prob1; tspan=(0.0,2.0))
A general syntax of
modified_problem = remake(original_problem; field_1 = value_1, field_2 = value_2, ... )
value_N are renamed to appropriate field names and new desired values.